Paper: using HFD to get a good understanding of the relationships between the Covid-19 measurements and the other covariates. we did this by breaking the signal down into three components. (1) the trend of the data. this is created using a loess smoothing. (2) the first difference of the trend. (3) the detrended data. this captures the noise processes. furthermore there is two view of the data. We look at the normal data and the log of data. The log of the data better captures the shape of Wastewater. at the bottom of the document contain plots showing a comprehensive view of the problem. The main goal of this document is to show the main takeaways of those plots in an easier way to see. The main takeaways are, 1) the covariates don’t strongly relate to the covid signal. 2) Crp and HF183 are strongly related. 3)

The table below shows the correlation between the Covid-19 signals and the covariate components. The baseline these covariates are meant to control for is population so Let’s first look at that. We can see in the original data it has a low correlation but in the log data it has a .3 correlation which is meaningful. This is larger then most of the covariates correlation which suggests that at least when working with the log of the data covariates other than population are not necessary. With the original data the HF183 and CrP have correlation of .3 which might be worth understanding. None of the detrended data correlates meaningful supporting the view that they are mostly caused by noise.

## # A tibble: 7 × 5
##   term            log_N1_Trend log_N2_Trend  N1_Diff N2_Diff
##   <chr>                  <dbl>        <dbl>    <dbl>   <dbl>
## 1 pop                  0.234        0.288    0.00155 -0.0119
## 2 log_PMMOV_Trend      0.213        0.171   -0.0170  -0.0133
## 3 log_HF183_Trend      0.287        0.227   -0.00854 -0.0258
## 4 log_CrP_Trend        0.211        0.179   -0.00868 -0.0178
## 5 PMMOV_Diff           0.0785       0.0755   0.00312  0.0163
## 6 HF183_Diff          -0.0247      -0.0265   0.0807   0.0613
## 7 CrP_Diff            -0.00671     -0.00292  0.0279   0.0295
## # A tibble: 7 × 5
##   term        N1_Trend N2_Trend    N1_Diff  N2_Diff
##   <chr>          <dbl>    <dbl>      <dbl>    <dbl>
## 1 pop           0.0659   0.119   0.0000270 -0.0253 
## 2 PMMOV_Trend   0.0654   0.0580 -0.000285   0.00341
## 3 HF183_Trend   0.365    0.371  -0.0214    -0.0640 
## 4 CrP_Trend     0.328    0.332  -0.0275    -0.0466 
## 5 PMMOV_Diff    0.0190   0.0112 -0.00669   -0.00436
## 6 HF183_Diff   -0.0134  -0.0230  0.00220   -0.00223
## 7 CrP_Diff     -0.0269  -0.0372  0.00290    0.0551